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It is common to use the electron density to partition a molecular system into atomic regions. The necessity for such a partitioning scheme is rooted in the unquestionable role of atoms in chemistry. Nevertheless, atomic properties are not well- defined concepts within the domain of quantum mechanics, as they are not observable. This has resulted in a proliferation of different approaches to retrieve the concept of atoms in molecules (AIM) within the domain of quantum mechanics and in silico experiments based on various flavors of model theories. One of the most popular families of models is the Hirshfeld, or stockholder, partitioning methods. Hirshfeld methods do not produce sharp atomic boundaries, but instead distribute the molecular electron density at each point between all the nuclear centers constituting the molecule. The various flavors of the Hirshfeld scheme differ mainly in how the atomic shares are computed from a reference promolecular density and how the reference promolecular density is defined. We first establish the pervasiveness of the Hirshfeld portioning by extending its information-theoretic framework. This characterizes the family of f-divergence measures as necessary and sufficient for deriving Hirshfeld scheme. Then, we developed a variational version of Hirshfeld partitioning method, called Additive Variational Hirshfeld (AVH). The key idea is finding the promolecular density, expanded as a linear combination of charged and neutral spherically-averaged isolated atomic densities in their ground and/or excited states, that resembles the molecular density as much as possible. Using Kullback-Liebler divergence measure, this automatically guarantees that each atom and proatom have the same number of electrons, and that the partitioning is size consistent. The robustness of this method is confirmed by testing it on various datasets. Considering the mathematical properties and our numerical results, we believe that AVH has the potential to supplant other Hirshfeld partitioning schemes in future. / Thesis / Doctor of Philosophy (PhD)

To describe the diffusion of atoms in the crystal lattice of a metal, we use the statistical model, which was previously well tested for the description of thermionic emission [1]. Atoms in the crystal lattice of a metal are held by large attractive forces, therefore the potential energy of moving, i.e. diffusing atoms is greater than the potential energy of the atoms of the crystal lattice by the value of u — the activation energy of the diffusion process.

No / We present a demonstrative application of the nonholonomic control method to a real physical system composed of two cold Cesium atoms. In particular, we show how to implement a CNOT quantum gate in this system by means of a controlled Stark field.

<p dir="ltr">In this work we investigate the existence and experimentally measurable properties of Majorana quasiparticles in a few-body number conserving atomic system.</p>

Tesis por compendio / Las especies de metal con diferentes tamaños (átomos individuales, nanocristales y nanopartículas) muestran un comportamiento catalítico diferente para diversas reacciones catalíticas heterogéneas. Se ha demostrado en la bibliografía que muchos factores que incluyen el tamaño de partícula, la forma, la composición química, la interacción metal-soporte, la interacción metal-reactivo / disolvente, pueden tener influencias significativas sobre las propiedades catalíticas de los catalizadores metálicos. Los desarrollos recientes de metodologías de síntesis bien controladas y herramientas de caracterización avanzada permiten correlacionar las relaciones a nivel molecular. En esta tesis, he llevado a cabo estudios sobre catalizadores metálicos desde átomos individuales hasta nanoclusters y nanopartículas. Al desarrollar nuevas metodologías de síntesis, el tamaño de las especies metálicas puede modularse y usarse como catalizadores modelo para estudiar el efecto del tamaño sobre el comportamiento catalítico de los catalizadores metálicos para la oxidación del CO, la hidrogenación selectiva, la oxidación selectiva y la fotocatálisis. Se ha encontrado que, los átomos metálicos dispersados por separado y los grupos subnanométricos de metal pueden aglomerarse en nanoclusters o nanopartículas más grandes en condiciones de reacción. Para mejorar la estabilidad de los catalizadores subnanométricos de metal, he desarrollado una nueva estrategia para la generación de átomos individuales y clusters en zeolitas. Esas especies subnanométricas de metales son estables en tratamientos de oxidación-reducción a 550 oC. Siguiendo esta nueva metodología de síntesis, este nuevo tipo de materiales puede servir como catalizador modelo para estudiar la evolución de especies subnanométricas de metales en condiciones de reacción. La transformación estructural de las especies subnanométricas de Pt ha sido estudiada mediante microscopía electrónica de transmisión in situ. Se ha demostrado que el tamaño de las especies de Pt está fuertemente relacionado con las condiciones de reacción, que proporcionan importantes conocimientos para comprender el comportamiento de los catalizadores de metales subnanométricos en condiciones de reacción. En la otra línea de investigación para catalizadores de metales no nobles, he desarrollado varias estrategias generales para obtener catalizadores de metales no nobles, ya sea soportados sobre óxidos metálicos o protegidos por capas delgadas de carbono. Estos materiales muestran un rendimiento excelente para varias reacciones importantes, como la hidrogenación quimioselectiva de nitroarenos, incluso cuando se comparan con los catalizadores de metales nobles convencionales. En algunos casos, los catalizadores de metales no nobles pueden incluso alcanzar selectividades para productos inviables que no ha sido posible conseguir en catalizadores de metales nobles convencionales, que es causado por la diferente ruta de reacción en catalizadores de metales no nobles. Sin embargo, la espectroscopía fotoelectrónica de rayos X a presión ambiente ha revelado que la irradiación de la luz puede modular la selectividad a los alcoholes y los hidrocarburos C2 +, lo que abre una nueva posibilidad para ajustar el comportamiento catalítico de los catalizadores metálicos. Con base en los trabajos anteriores de diferentes aspectos relacionados con catalizadores metálicos heterogéneos, las perspectivas sobre las direcciones futuras hacia una mejor comprensión del comportamiento catalítico de diferentes entidades metálicas (átomos individuales, nanoagrupamientos y nanopartículas) de una manera unificadora también se han dado en esta tesis. / Les espècies metàl·liques de diferents dimensions (àtoms individuals, nanoclusters i nanopartícules) mostren diferents comportaments catalítics per a diverses reaccions catalítiques heterogènies. S'ha demostrat a la literatura que, molts factors que inclouen la mida de la partícula, la forma, la composició química, la interacció amb el suport metàl·lic, la reacció metàl·lica i la interacció amb dissolvents poden tenir influències significatives sobre les propietats catalítiques dels catalitzadors metàl·lics. Els desenvolupaments recents de metodologies de síntesi ben controlades i eines de caracterització avançada permeten relacionar les relacions a nivell molecular. En aquesta tesi, he realitzat estudis sobre catalitzadors metàl·lics d'àtoms únics a nanoclústers i nanopartícules. Mitjançant el desenvolupament de noves metodologies de síntesi, la mida de les espècies metàl·liques es pot modular i utilitzar com a catalitzadors model per estudiar l'efecte de mida sobre el comportament catalític dels catalitzadors metàl·lics per a l'oxidació de CO, hidrogenació selectiva, oxidació selectiva i fotocatàlisi. S'ha trobat que, els àtoms metàl·lics dispersos individualment i els clústers metàl·lics subnanomètrics poden aglomerar-se en nanoclústeres o nanopartícules més grans en condicions de reacció. Per millorar l'estabilitat dels catalitzadors subnanomètrics de metall, he desenvolupat una nova estratègia per a la generació d'àtoms i racimos en zeolites. Aquestes espècies metàl·liques subnanométricas són estables en tractaments de reducció d'oxidació a 550 oC. Després d'aquesta nova metodologia de síntesi, aquest nou tipus de materials poden servir com a model de catalitzador per estudiar l'evolució de les espècies metàl·liques subnanométricas en condicions de reacció. La transformació estructural de l'espècie Pn subnanométrica ha estat estudiada per microscòpia electrònica de transmissió in situ. S'ha demostrat que la mida de les espècies de Pt està fortament relacionada amb les condicions de reacció, que proporcionen idees importants per comprendre el comportament dels catalitzadors de subnanometria en condicions de reacció. En l'altra línia de recerca dels catalitzadors de metalls no nobles, he desenvolupat diverses estratègies generals per obtenir catalizadors de metalls no nobles recolzats en òxids metàl·lics o protegits per capes de carboni primes. Aquests materials presenten un excel·lent rendiment per a diverses reaccions importants, com la hidrogenació quimioelectiva de nitroarenes, fins i tot quan es comparen amb els catalitzadors convencionals de metall noble. En alguns casos, els catalitzadors de metalls no nobles poden fins i tot aconseguir selectivitats a productes no factibles que no s'han pogut assolir en catalitzadors de metall noble convencionals, que es deuen a la via de reacció diferent en catalitzadors de metalls no nobles. No obstant això, s'ha observat una espectroscòpia de fotoelèctria de raigs X amb pressió d'atmosfera que la irradiació lleugera pot modular la selectivitat als alcohols i hidrocarburs C2 +, la qual cosa obre una nova possibilitat per sintonitzar el comportament catalític dels catalitzadors metàl·lics. A partir d'aquests treballs de diferents aspectes relacionats amb els catalitzadors metàl·lics heterogenis, també s'ha donat en aquesta tesi perspectives sobre les futures orientacions cap a una millor comprensió del comportament catalític de diferents entitats metàl·liques (àtoms individuals, nanoclústers i nanopartícules). / Metal species with different size (single atoms, nanoclusters and nanoparticles) show different catalytic behavior for various heterogeneous catalytic reactions. It has been shown in the literature that, many factors including the particle size, shape, chemical composition, metal-support interaction, metal-reactant/solvent interaction, can have significant influences on the catalytic properties of metal catalysts. The recent developments of well-controlled synthesis methodologies and advanced characterization tools allow to correlate the relationships at molecular level. In this thesis, I have carried out studies on metal catalysts from single atoms to nanoclusters and nanoparticles. By developing new synthesis methodologies, the size of metal species can be modulated and used as model catalysts to study the size effect on the catalytic behavior of metal catalysts for CO oxidation, selective hydrogenation, selective oxidation and photocatalysis. It has been found that, singly dispersed metal atoms and subnanometric metal clusters may agglomerate into larger nanoclusters or nanoparticles under reaction conditions. To improve the stability of subnanometric metal catalysts, I have developed a new strategy for the generation of single atoms and clusters in zeolites. Those subnanometric metal species are stable in oxidation-reduction treatments at 550 oC. Following this new synthesis methodology, this new type of materials can serve as model catalyst to study the evolution of subnanometric metal species under reaction conditions. The structural transformation of subnanometric Pt species has been studied by in situ transmission electron microscopy. It has been shown that the size of Pt species is strongly related with the reaction conditions, which provide important insights for understanding the behavior of subnanometric metal catalysts under reaction conditions. In the other research line for non-noble metal catalysts, I have developed several general strategies to obtain non-noble metal catalysts either supported on metal oxides or protected by thin carbon layers. These materials show excellent performance for several important reactions, such as chemoselective hydrogenation of nitroarenes, even when compared with conventional noble metal catalysts. In some cases, non-noble metal catalysts can even achieve selectivities to unfeasible products which has not been possible to achieve on conventional noble metal catalysts, which is caused by the different reaction pathway on non-noble metal catalysts. Nevertheless, it has been revealed by ambient-pressure X-ray photoelectron spectroscopy that light irradiation can modulate the selectivity to alcohols and C2+ hydrocarbons, which opens a new possibility for tuning the catalytic behavior of metal catalysts. Based on the above works from different aspects related with heterogeneous metal catalysts, perspectives on the future directions towards better understanding on the catalytic behavior of different metal entities (single atoms, nanoclusters and nanoparticles) in a unifying manner have also been given in this thesis. / Liu, L. (2018). Heterogeneous Metal Catalysts: From Single Atoms to Nanoclusters and Nanoparticles [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/113169 / Compendio

Pt-supported catalysts are widely used industrially for hydrogenation reactions. However, the kinetics of hydrogen activation, a critical step for any hydrogenation reaction, is still not well understood on supported Pt surfaces. Recent studies had shown that activity and selectivity vary with Pt nuclearity for the acetylene semihydrogenation reaction, increasing in activity and decreasing in selectivity while increasing the particle size from single atoms (SA) to sub-nanoclusters to nanoparticles (NP), attributing the cause of these differences on activities to the activity of H2 activation in the H/D isotopic exchange reaction. In this work, the kinetics of H2 is studied by performing the H2-D2 isotopic exchange reaction on Pt-supported catalysts with different nuclearity to extract the activation barriers and pre-exponential factors for dissociating adsorption and associative desorption (Eads, Edes, and vads, vdes respectively) from the microkinetic model derived from the Bonhoeffer Farkas mechanism, this to perform a more in-depth analysis regarding the differences in activity when comparing the H2 adsorption energy (Eads+ = Eads-Edes) and frequency factors as a function of nuclearity. Experiments were carried out in a quartz tubular fixed bed reactor coupled with a Mass Spectrometer to analyze the product gas by carrying out both, an integral analysis (from 0 to equilibrium conversion) by performing light-off experiments and differential analysis (low conversions) by performing Arrhenius experiments in the low and high coverage regions. / Master of Science / Hydrogenation is a chemical reaction widely used in the petrochemical industry for the refining process where a substance reacts with molecular hydrogen H2 adding pairs of H atoms to compounds. However, hydrogen is unreactive towards other substances in the absence of metal catalysts such as platinum (Pt), which dramatically accelerates the reaction rates making hydrogenation reaction possible. In industry, metallic catalysts are found as supported catalysts where the precious metal is supported on materials with higher thermal and mechanical stability to endure the operation conditions. Depending on the pretreatment conditions the size of metallic particles on the support can be manipulated, giving place to samples made of the same materials but different particle sizes with different properties. There are two critical steps during hydrogenation reactions the first one is the hydrogen activation which consists of the dissociation and adhesion of the two hydrogen atoms from the molecular hydrogen on the metallic surface and the second one is the reverse process where two hydrogen atoms recombine and are released from the metallic surface. Both steps involve a minimum amount of energy to dissociate and recombine hydrogen atoms which are strongly dependent on the metallic particle sizes. The goal of this thesis is to extract these dissociation and recombination energies of hydrogen on platinum particles of different sizes supported on alumina.

In this dissertation, we use exact diagonalization to study a few strongly correlated systems, ranging from the Fermi-Hubbard model to the fractional quantum Hall effect (FQHE). The discussion starts with an overview of strongly correlated systems and what is meant by strongly correlated. Then, we extend cluster perturbation theory (CPT), an economic method for computing the momentum and energy resolved Green's function for Hubbard models to higher order correlation functions, specifically the spin susceptibility. We benchmark our results for the one-dimensional Fermi-Hubbard model at half-filling. In addition we study the FQHE at fillings $nu = 5/2$ for fermions and $nu = 1/2$ for bosons. For the $nu = 5/2$ system we investigate a two-body model that effectively captures the three-body model that generates the Moore-Read Pfaffian state. The Moore-Read Pfaffian wave function pairs composite fermions and is believed to cause the FQHE at $nu = 5/2$. For the $nu = 1/2$ system we estimate the entropy needed to observe Laughlin correlations with cold atoms via an ansatz partition function. We find entropies achieved with conventional cooling techniques are adequate. / Doctor of Philosophy / Strongly correlated quantum many-body physics is a rich field that hosts a variety of exotic phenomena. By quantum many-body we mean physics that is concerned with the behavior of interacting particles, such as electrons, where the quantum behavior cannot be ignored. By strongly correlated, we mean when the interactions between particles are sufficiently strong such that they cannot be treated as a small perturbation. In contrast to weakly correlated systems, strongly correlated systems are much more difficult to solve. That is because methods that reduce the many-body problem to a single independent body problem do not work well. In this dissertation we use exact diagonalization, a method to computationally solve quantum many-body systems, to study two strongly correlated systems: the Hubbard model and the fractional quantum Hall effect.The Hubbard model captures the physics of many interesting materials and is the standard toy model. Originally developed with magnetic properties in mind, it has been extended to study superconductivity, topological phases, cold atoms, and much more. The fractional quantum Hall effect is a novel phase of matter that hosts exotic excitations, some of which may have applications to quantum computing.